Completeness of \({\mathcal L}^ p\) spaces and Radon-Nikodym theorems for unbounded finitely additive measures
type: Item
instance of: scholarly article
title: Completeness of \({\mathcal L}^ p\) spaces and Radon-Nikodym theorems for unbounded finitely additive measures
zbMATH Open document ID: 0889.28002
author: Wayne C. Bell
author: J. W. Hagood
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-03-04T00:00:00Z
review text: The authors characterize completeness of the Lebesgue spaces \({\mathcal L}^p(\Omega,{\mathcal F},\mu)\) for finitely additive measures \(\mu\) on the field \({\mathcal F}\) of subsets of a set \(\Omega\) in the bounded as well as in the unbounded case. Moreover, necessary and sufficient conditions are given by means of Hahn decompositions such that a signed finitely additive measure has a Radon-Nikodým derivative relative to a semidefinite finitely additive measure based on an integral by Maharam.
Mathematics Subject Classification ID: 28A12
Mathematics Subject Classification ID: 28A25
zbMATH DE Number: 1123512
zbMATH Keywords: Maharam integral
zbMATH Keywords: completeness of the Lebesgue spaces
zbMATH Keywords: finitely additive measures
zbMATH Keywords: Radon-Nikodým derivative
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5744
OpenAlex ID: W2035920580
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DOI: 10.1006/JMAA.1997.5744
description: scientific article; zbMATH DE number 1123512